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   \begin{table}[htbp] 
   \caption{\bf Pricing Ability:  local  PCA vs  IPCA }
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\begin{tabular}{lccccccc|} 
 $ \scriptsize{(N,T):}$ & (15,5)  & (15,25) &  (100,5) & (100,25) & (1,000,5) & (1,000,25) \\  \hline 
& \multicolumn{5}{c}{\scriptsize{\bf Experiment (A): Correct Model - Stationary Instruments} } & \\
  & \scriptsize{ (IPCA/local-PCA) } & \scriptsize{ (IPCA/local-PCA)  } & \scriptsize{(IPCA/local-PCA) } & \scriptsize{(IPCA/local-PCA)} & \scriptsize{(IPCA/local-PCA)} & \scriptsize{(IPCA/local-PCA) }  \\ 
 \scriptsize{
 In-Sample:} &    5.851   &  2.036 &   5.213 &    1.479  &  5.304 &   2.150 \\
 \scriptsize{ 
 Out-of-Sample:} &  1.137 &  1.009 &    1.454 &    1.487 &    1.223 &    2.130 \\  \hline
  & \multicolumn{5}{c}{\scriptsize{\bf Experiment (B): Misspecified Model - Stationary Instruments} } & \\
  & \scriptsize{ (IPCA/local-PCA) } & \scriptsize{ (IPCA/local-PCA)  } & \scriptsize{(IPCA/local-PCA) } & \scriptsize{(IPCA/local-PCA)} & \scriptsize{(IPCA/local-PCA)} & \scriptsize{(IPCA/local-PCA) }  \\ 
  \scriptsize{  
 In-Sample:}   &     11.668 &   3.891 &    6.997 &    2.764 &  10.023 &   3.204 \\
 \scriptsize{ 
 Out-of-Sample:} &     2.145  &   3.401 &    1.967 &    2.002 &   2.574 &    3.012 \\  \hline
   & \multicolumn{5}{c}{\scriptsize{\bf Experiment (C): Correct Model - Random Walk Instruments} } & \\
 & \scriptsize{ (IPCA/local-PCA) } & \scriptsize{ (IPCA/local-PCA)  } & \scriptsize{(IPCA/local-PCA) } & \scriptsize{(IPCA/local-PCA)} & \scriptsize{(IPCA/local-PCA)} & \scriptsize{(IPCA/local-PCA) }  \\
 \scriptsize{  
 In-Sample:} &  9.980 &   4.568  &    9.025 &    3.356 &   11.655 &    5.924 \\
 \scriptsize{ 
 Out-of-Sample:} &    1.681 &    3.494 &   1.942 &    2.849 &   2.077 &    4.436 \\ \hline
    \end{tabular}
    \parbox{7.0in}{\footnotesize{This table presents ratios of the pricing ability criterion $N^{-1}\sum_{i=1}^N \tilde{\delta}_{i}^2  $  corresponding to the IPCA  (numerator) and local-PCA  \newline (denominator),   averaged across $1,000$ Monte Carlo iterations,  and evaluated in-sample and out-of-sample,  for various  \newline  combinations of $(N,T)$. The data generating process is (15) %(\ref{ipca})
     where the vector ${\bf z }_{it-1}$ is a $10$-sized stationary VAR  \newline  (Experiment (A)) and a multivariate random walk (Experiment (C)), respectively. Experiment (B) differs from (A)  \newline  because the IPCA-estimated model is misspecified (one instrument instead of the $10$ required instruments).
}}
\label{Table1}
\end{table}



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